Related papers: Generalized Chen's conjecture for biharmonic maps …

f-Biharmonic maps are the extrema of the f-bienergy functional. f-biharmonic submanifolds are submanifolds whose defining isometric immersions are f-biharmonic maps. In this paper, we prove that an f-biharmonic map from a compact Riemannian…

In this paper, a general hybrid fixed point theorem for the contractive mappings in generalized Banach spaces is proved via measure of weak non-compactness and it is further applied to fractional integral equations for proving the existence…

In this paper, the description of biharmonic map equation in terms of the Maurer-Cartan form for all smooth map of a compact Riemannian manifold into a Riemannian symmetric space $(G/K,h)$ induced from the bi-invariant Riemannian metric $h$…

We study f-biharmonic and bi-f-harmonic submanifolds in both generalized complex and Sasakian space forms. We prove necessary and sufficient condition for f-biharmonicity and bi-f-harmonicity in the general case and many particular cases.…

A longstanding conjecture on biharmonic submanifolds, proposed by Chen in 1991, is that {\it any biharmonic submanifold in a Euclidean space is minimal}. In the case of a hypersurface $M^n$ in $\mathbb R^{n+1}$, Chen's conjecture was…

In this note we review some results on the transversality conditions for a smooth Fredholm map $f: X \times (0,T) \to Y$ between two Banach spaces $X,Y$. These conditions are well-known in the realm of bifurcation theory and commonly…

We consider topological conditions under which a locally invertible map admits a global inverse. Our main theorem states that a local diffeomorphism $f: M \to\mathbb{R}^n$ is bijective if and only if $H_{n-1}(M)=0$ and the pre-image of…

The Gy\'arf\'as tree packing conjecture asserts that any set of trees with $2,3, ..., k$ vertices has an (edge-disjoint) packing into the complete graph on $k$ vertices. Gy\'arf\'as and Lehel proved that the conjecture holds in some special…

We prove several unique continuation results for biharmonic maps between Riemannian manifolds.

In this paper, we study the Bergman kernel $B_\varphi(x,y)$ of generalized Bargmann-Fock spaces in the setting of Clifford algebra. The versions of $L^2$-estimate method and weighted subharmonic inequality for Clifford algebra are…

In the present paper, we prove generalizations of Banach, Kannan, Chatterjea, \'Ciri\'c-Reich-Rus fixed point theorems, as well as of the fixed point theorem for mappings contracting perimeters of triangles. We consider corresponding…

We prove the Strengthened Hanna Neumann Conjecture. We give a more direct cohomological interpretation of the conjecture in terms of "typical" covering maps, and use graph Galois theory to "symmetrize" the conjecture. The conjecture is then…

We extend the Marcus-Schaeffer bijection between orientable rooted bipartite quadrangulations (equivalently: rooted maps) and orientable labeled one-face maps to the case of all surfaces, that is orientable and non-orientable as well. This…

We give a different presentation of a recent bijection due to Chapuy and Dol\k{e}ga for nonorientable bipartite quadrangulations and we extend it to the case of nonorientable general maps. This can be seen as a Bouttier--Di…

Recently, harmonic functions and frequently universal harmonic functions on a tree $T$ have been studied, taking values on a separable Fr\'{e}chet space $E$ over the field $\mathbb{C}$ or $\mathbb{R}$. In the present paper, we allow the…

In this paper, we will give an extension of Mok's theorem on the generalized Frankel conjecture under the condition of the orthogonal bisectional curvature.

Let $X, Y$ be two complex manifolds, let $D\subset X,$ $ G\subset Y$ be two nonempty open sets, let $A$ (resp. $B$) be an open subset of $\partial D$ (resp. $\partial G$), and let $W$ be the 2-fold cross $((D\cup A)\times B)\cup…

We show that Generic Green's conjecture holds for generic binary curves, through a detailed analysis of the family of scrolls containing fixed rational normal curves.

The aim of this paper is to construct a fractal with the help of a finite family of generalized F-contraction mappings, a class of mappings more general than contraction mappings, defined in the setup of b-metric space. Consequently, we…

We use motivic methods to give a quick proof of Berthelot's conjecture stating that the push-forward map in rigid cohomology of the structural sheaf along a smooth and proper map has a canonical structure of overconvergent F-isocrystal on…